Problem: $80$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $68$ less than $3$ times the number of away team fans. How many home team and away team fans attended the game?
Answer: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 80}$ ${x = 3y-68}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${3y-68}$ for $x$ in the first equation. ${(3y-68)}{+ y = 80}$ Simplify and solve for $y$ $ 3y-68 + y = 80 $ $ 4y-68 = 80 $ $ 4y = 148 $ $ y = \dfrac{148}{4} $ ${y = 37}$ Now that you know ${y = 37}$ , plug it back into ${x = 3y-68}$ to find $x$ ${x = 3}{(37)}{ - 68}$ $x = 111 - 68$ ${x = 43}$ You can also plug ${y = 37}$ into ${x+y = 80}$ and get the same answer for $x$ ${x + }{(37)}{= 80}$ ${x = 43}$ There were $43$ home team fans and $37$ away team fans.